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11 Feb 2019, 02:44

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Difficulty:

75% (hard)

Question Stats:

49%(03:08) correct 51%(02:31) wrong based on 49 sessions

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One-third of all U. S. taxpayers may deduct charitable contributions on their federal income tax returns. Forty percent of all taxpayers may deduct state income tax payments from their federal returns. If 55 percent of all taxpayers may not deduct either charitable contributions or state income tax, what portion of all taxpayers may claim both types of deductions?

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11 Feb 2019, 03:23

Bunuel wrote:

One-third of all U. S. taxpayers may deduct charitable contributions on their federal income tax returns. Forty percent of all taxpayers may deduct state income tax payments from their federal returns. If 55 percent of all taxpayers may not deduct either charitable contributions or state income tax, what portion of all taxpayers may claim both types of deductions?

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15 Feb 2019, 23:38

Solved using venn diagram approach and simplifying the equationlet the total pop be xthus \(\frac{x}{3}+\frac{4x}{10}- y = \frac{45x}{100}\), where y = who can claim bothsolve the equation and thus \(\frac{y}{x}=\frac{17}{60}\).Thus answer E
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16 Feb 2019, 16:45

It's a pure ratio question, so we can invent a total number and use it to answer the question. 300 is convenient, since we want to be able to divide our total both by 3 and by 100. Then we know 45% of these, or 135 people, can make some kind of deduction; 100 can make a federal deduction; and 120 can make a state deduction. So we have a standard Venn diagram situation:

- x people can make both deductions, so are in the overlapping part of the Venn diagram- 100-x people are in the federal deductions *only* region of the diagram- 120-x people are in the state deductions *only* region of the diagram

Since these three things must add up to the total number of people, 135, in the two circles, we have

220 - x = 135x = 85

and 85/300 = 17/60 is the answer.
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17 Feb 2019, 00:03

Bunuel wrote:

One-third of all U. S. taxpayers may deduct charitable contributions on their federal income tax returns. Forty percent of all taxpayers may deduct state income tax payments from their federal returns. If 55 percent of all taxpayers may not deduct either charitable contributions or state income tax, what portion of all taxpayers may claim both types of deductions?

(A) 3/20(B) 9/50(C) 1/5(D) 7/25(E) 17/60

Well I see that many people like me are choosing D. It took me almost 10 mins to realize the mistake

So we know that:Number of taxpayers who deduct charitable contributions = CCd = 1/3Number of taxpayers who deduct state income tax = SId = 40% = 2/5Number of taxpayers who dont deduct either = 55/100=> Number of taxpayers who deduct both = Td = 45/100Let us assume the overlap between CCd and SId to be x